`x_(1) , x_(2) , x_(3)`… . `x_(50)` are fifty real numbers such that `x_(r) lt x_(r + 1)` for r = 1 ,2 , 3 …….. , 49 . Five numbers out of these are picked up at random . The probability that the five numbers have `x_(20)` as the middle number is :

If x_(1),x_(2),x_(3),x_(4),x_(5) are five consecutive odd numbers then their average is

If x is a real number and |x| lt 3 , then

If x_(1),x_(2),x_(3) and x_(4) are positive real numbers such that x_(1)x_(2)x_(3)x_(4)=1, then the least value of (1+x_(1))(1+x_(2))(1+x_(3))(1+x_(4)) is

If a number x is chosen at random from the numbers -2,-1,0,1,2. What is the probability that x^(2)<2?

A number x is chosen from the numbers -3.2 .-1,0,1,2. Find the probability that x^(2)<=4

If a number x is chosen at random from the number -2, -1, 0, 1, 2. What is the probability that x^(2)lt2 ?

If a is real number such that 0 lt alt 1 , show that the function f(x) = a^(x) is strictly decreasing on R.

A number x is chosen at random from the set S = (1, 2, 3,....,100).Then the probability that the expression sqrt((x-15)/((x-10)(x-20))) is a positive real number is

Statement-1 : Three natural number are taken at random from the set A={x:1 lt x lt= 100, x in N} the probability that the A.M of the numbers taken is 25 is equal to (""^74C_2)/(""^100C_3) . Statement-2 : Let A = {2, 3, 4 …. 20}. A number is chosen at random from set A and it is bound to be a prime number. The probability that it is more than 10 is 1/5 . Statement-3 : The probability of three person having the same date month for the birthday is 1/((365)^2) .